Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

TL;DR

This paper investigates the mechanics of bistable elements in soft morphable sheets, revealing how their design influences global shape bifurcations and enabling more controlled reprogrammability in elastic metamaterials.

Contribution

It provides a detailed analysis of a single bistable element's behavior and demonstrates how lattice design can delay shape bifurcations in soft morphable sheets.

Findings

Boundary layer analysis explains bistability deformation

Lattice design can delay shape bifurcation

Single element behavior informs global shape control

Abstract

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat 'skirt' region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.